MIDTERM 2

Question 1

what are the names of all the common ionic latices?

Answer 1

• CsCl
• rock salt (NaCl)
• wurtzite (ZnS)
• zinc blende (ZnS)
• fluorite (CaF2)
• perovskite (ABX3)

Question 2

what is the CN and structure of CsCl?

Answer 2

CN = 8
Structure = bcc

Question 3

what is the CN and structure of rock salt?

Answer 3

CN = 6 
Structure = ccp/fcc with cation in all O holes

Question 4

what is the CN and structure of zinc blende?

Answer 4

CN = 4
Structure = ccp/fcc with cation in half T holes

Question 5

what is the CN and structure of wurtzite?

Answer 5

CN = 4
Structure = hcp with cation in half T holes

Question 6

what is the CN and structure of Fluorite?

Answer 6

CN = 8:4 (cation:anion)
Structure = ccp/fcc with anion in all T holes

Question 7

what is the structure of perovskite?

Answer 7

Structure = normal ccp/fcc arrangement between cations & anions, but there’s a single cation in middle of cube (like bcc structure) - single cation sits in 1/4 of O holes

Question 8

what is the approximate radius ratio value of CN = 8?

Answer 8

r+/r- = 0.7

Question 9

what is the approximate radius ratio value of CN = 6?

Answer 9

r+/r- = 0.4

Question 10

what is the approximate radius ratio value of CN = 4?

Answer 10

r+/r- = 0.2

Question 11

what is the approximate radius ratio value of CN = 3?

Answer 11

r+/r- = 0.15

Question 12

when is Z+ and Z- in born-mayer equation changing?

Answer 12

when comparing 2 different ionic solids with different cation and anion charges

Question 13

what is r0 in born-mayer equation changing?

Answer 13

when comparing 2 different ionic solids that have the same anion and cation charges, but they’re “electron clouds” are different sizes - aka. small molecules therefore with low amount of orbitals vs. larger molecules therefore with more orbitals (produces non-ionic r0)

Question 14

when can’t the born-mayer equation predict a molecule’s stability?

Answer 14

when its either a polarizable atom/element OR the bonding isn’t ionic (non-ionic r0)

Question 15

what elements are polarizable?

Answer 15

• large anions OR small cations with high charges

Question 16

how to tell which molecule is more stable using the born-mayer equation?

Answer 16

the one with the larger U(r0) value

Question 17

what is a schottky defect?

Answer 17

intrinsic (stoichiometric) defect where one anion & cation are randomly missing from rock salt structure

Question 18

what is a frenkel defect?

Answer 18

intrinsic (stoichiometric) defect where an ion is displaced off lattice site & fills another site that is normally empty

Question 19

what is an extrinsic defect?

Answer 19

doping with vacancies

Question 20

what are p-doped and n-doped semiconductors?

Answer 20

intentionally added point defects

Question 21

what is a substitutional solid?

Answer 21

a point defect where an ion from outside structure directly replaces an ion of same charge

Question 22

what is an interstitial solid?

Answer 22

a point defect where small ions enter empty interstitial sites (spaces between lattice)

Question 23

what is an edge dislocation?

Answer 23

plane of atoms that goes part way through the structure (looks like wood grain)

Question 24

what is a screw dislocation?

Answer 24

slip of plane in crystal structure (looks like staircase OR atoms sitting directly on top of each other)

Question 25

what is the schrodinger equation for a 1D box?

Answer 25

(−h2)/(8π^2 m)∗d^2/(dx^2 ) Ψ(x) = EΨ(x)

Question 26

what does a general wavefunction look like?

Answer 26

Ψ(x)=asin⁡(nπx/L) OR Ψ(x)=asin⁡(2πx/λ)

Question 27

what does a general eigenvalue look like?

Answer 27

-(2π / λ)^2 * asin⁡(2πx/λ)

Question 28

what does the Ĥ operator look like?

Answer 28

(−h2)/(8π^2 m)∗d^2/(dx^2 )

Question 29

what is a in the schrodinger equation?

Answer 29

√(2/L)

Question 30

what does the normalization factor look like?

Answer 30

a^2 (L/2)=1

Question 31

what does a laplacian look like?

Answer 31

∇^2=(−h^2)/(8π^2 m)

Question 32

what are the radial and angular parts of the wavefunction?

Answer 32

radial = R(r) 
angular = Y(θ,Φ)

Question 33

describe what energy is used in the particle in a box model?

Answer 33

• only specific values of energy allowed (V = 0 and V = ∞) therefore only kinetic energy is used
• kinetic energy = T=h2/(2me λ^2 )

Question 34

describe what wavelengths are allowed in the particle in a box model?

Answer 34

1/2 cycle λ = 2L
1 cycle λ = L
1 & 1/3 cycle λ = 2L/3
2 cycles λ = L/2

Question 35

energy (T) differences between allowed differences in particle in a box model?

Answer 35

1/2 cycle (T1) = h2/(2me) * (1/4L^2)
1 cycle (T2) = 4 T1
1 & 1/3 cycle (T3) = 9 T1
2 cycles (T4) = 16 T1